Chapter 6 Practice | Complete Solution

Chapter 6 Practice

Question 1

If x is uniformly distributed over the interval 8 to 12, inclusively (8 ≤ x ≤ 12), then the probability, P(13 ≤ x ≤ 15), is ____________ .

Question 2

If x is uniformly distributed over the interval 8 to 12, inclusively (8 ≤ x ≤ 12), then P(x ≥ 10) is _____________ .

Question 3

If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 ≤ x ≤ 30), then the probability that an oil change job is completed in 21.75 to 24.25 minutes, inclusively, i.e., P(21.75 ≤ x ≤ 24.25) is ____________ .

Question 4

Let z be a normally distributed random variable with mean 0 and standard deviation 1. What is P(z < 1.3)?

Question 5

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?

Question 6

Within a range of z scores from -1 to +1, you can expect to find ______ percent of the values in a normal distribution.

Question 7

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?

Question 8

The net profit of an investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor's net gain will be at least $5,000 is ___________ .

Question 9

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.5 inches and a standard deviation of 0.2 inches.What is the probability that a sheet selected at random will be less than 31 inches long?

Question 10

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.
What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?

Question 11

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces?

Question 12

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received weekly be between 180 and 210?

Question 13

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

Question 14

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?

Question 15

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

Question 16

A negative value of Z indicates that

Question 17

The center of a normal curve is

Question 18

Which of the following is not a characteristic of the normal probability distribution?

Question 19

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 241.25 pounds is

Question 20

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing less than 250 pounds is

Question 21

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What percent of players weigh between 180 and 215 pounds?

Question 22

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.What is the minimum weight of the middle 95% of the players? (HINT: Apply the Empirical Rule to solve this question)